6. Consider a spring-mass system with small damping and driven by a cosine force: x" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0. Find the solution and plot the result.
6. Consider a spring-mass system with small damping and driven by a cosine force: x" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0. Find the solution and plot the result.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 70E
Related questions
Question
Please do number 6
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0.5
0
-0.5
-1
-1.5
-2
0
0.5
1
1.5
2
1
2.5
3
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Figure 2.9 Plot of the solution r(t) = 10-³ (cos(45t) - cos(55t)) to Exercise
7(c) showing the phenomenon of beats.
Find the solution and plot the result.
7. Consider the equation
4
4. Consider a general LC circuit with input voltage Vo sin ßt. If 8 and the
capacitance C are known, what value of the inductance L causes pure
resonance?
5. An undamped spring-mass system with m = 4 and and stiffness k is forced
by a sinusoidal function 412 sin 5t. What value of k causes pure resonance?
6. Consider a spring-mass system with small damping and driven by a cosine
force:
x" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0.
x"+w²x = cos Bt.
a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when
w‡ B.
= cos(A-B)-cos(A+B)
b) Use the trigonometric identity 2 sin Asin B =
to write the solution as a product of sines.
c) Take w = 55 and
= 45 and plot the solution from part (b) on
the time interval [0, 4]. The solution can be interpreted as a high fre
quency response contained in a low frequency amplitude envelope. We](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc10cce41-ef51-4545-a724-9736e236d3b7%2F5f7dca60-da48-4cba-b2a9-c720bd742474%2Feou0k4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2t.
ady-
ded,
ero
ral
de
0.5
0
-0.5
-1
-1.5
-2
0
0.5
1
1.5
2
1
2.5
3
3.5
Figure 2.9 Plot of the solution r(t) = 10-³ (cos(45t) - cos(55t)) to Exercise
7(c) showing the phenomenon of beats.
Find the solution and plot the result.
7. Consider the equation
4
4. Consider a general LC circuit with input voltage Vo sin ßt. If 8 and the
capacitance C are known, what value of the inductance L causes pure
resonance?
5. An undamped spring-mass system with m = 4 and and stiffness k is forced
by a sinusoidal function 412 sin 5t. What value of k causes pure resonance?
6. Consider a spring-mass system with small damping and driven by a cosine
force:
x" +0.01x' + 4x = cos 2t, x(0) = 0, x'(0) = 0.
x"+w²x = cos Bt.
a) Find the solution when the initial conditions are x(0) = x'(0) = 0 when
w‡ B.
= cos(A-B)-cos(A+B)
b) Use the trigonometric identity 2 sin Asin B =
to write the solution as a product of sines.
c) Take w = 55 and
= 45 and plot the solution from part (b) on
the time interval [0, 4]. The solution can be interpreted as a high fre
quency response contained in a low frequency amplitude envelope. We
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